Question

In: Math

Create your own scenario in which you can compare the cost for two choices for the...

Create your own scenario in which you can compare the cost for two choices for the same service.

You will need to create two equations, each of which should include::

1. fixed cost

2. variable cost

Then write an inequality to compare the two choices and solve it. Interpret your solution to further explain your comparison. Below is an example that you may use as a model to help you develop your own scenario.

I am trying to decide whether to install a solar energy system or replace my existing gas system. The solar system will cost $20,000 to install but only $25 per month. The equation for the total cost is Solar Cost = 25x + 20000 where x is the number of months. The gas system will only cost $5,000 to install but will cost $125 per month. The equation is Gas Cost = 125x + 5000. To find out how long I need to live in my home for the solar to be more cost effective, I need to solve the following inequality: 25x + 20000 < 125x + 5000. When I solve the inequality, x > 150. That means I need to live in the house longer than 150 months, or 12.5 years, for the solar system to be a better deal.

Solutions

Expert Solution

Solar system:

Fixex cost=Installation cost= $20,000

Variable cost= $25 per month

Let x be the number of months.

Variable cost= 25*x=25x

Total cost = Fixed cost+ Variable cost

Total cost of solar sytem= 20,000+25x

Gas system:

Fixex cost=Installation cost= $5,000

Variable cost= $125 per month

Let x be the number of months.

Variable cost=125*x=125x

Total cost = Fixed cost+ Variable cost

Total cost of solar sytem= 5000+125x

For the solarsystem to be beneficial,

cost of solar system< cost of gas system

20,000+25x<5000+125x

subtracting 20,000 from both sides

20,000+25x-20,000<5,000+125x-20,000

25x<125x-15,000

Subtract 125x from both sides

25x-125x<125x-15,000-125x

-100x<-15,000

Multiplying with (-1) on both sides and reversing the inequality

-100x*(-1)>-15,000*(-1)

100x>15,000

Dividing with 100 on both sides

x>150

150 months =12.5 years

So , we should live more than 150 months (12.5 years)in the house for the solar sytem to be benificial.

If we are living less than 12.5 years in the house then the gas system will be benificial.

milcah answered 1 year ago

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